Equation of a Line

Concept Quizzes

Challenge Quizzes

Equation of a Line: Level 4 Challenges

Given that a straight line in the \(xy\)-plane passes through the point \((3,48)\) in the first quadrant and intersects the positive \(x\)- and \(y\)-axes at points \(P\) and \(Q\) respectively. Let \(O\) designate the origin.

The line \(4x + y = 1\) passes through the point \(A(2,-7)\) and intersects point \(B\) on the line \(BC\) whose equation is \(3x - 4y + 1=0\). The equation of the line \(AC\) is \(ax + by + c = 0\) (with \(a,\) \(b,\) and \(c\) all coprime) and constructed so that the distance from \(A\) to \(B\) is the same as the distance from \(A\) to \(C\).

Given that a straight line in the \(xy\)-plane passes through the point \((3,48)\) in the first quadrant and intersects positive \(x\)- and \(y\)-axes at points \(P\) and \(Q\) respectively. Let \(O\) designate the origin.